But how about "Europe"? Tally the European Union medals and you get a whopping 306, ranging from Britain (65) to Portugal (1). In London, EU athletes ran, swam, jumped, and pole-vaulted with passion on behalf of their nations and programs. But none of these Olympians talked about winning for the EU.

And therein lies a conundrum for the sprawling entity known as Europe. Despite an abstract pride Europeans feel in being from the EU, the emotion, drive, and thrill of victory is still largely national. You do it for your flag.

On the sports field, this is positive and natural, and no one wants to change it. But in the world of politics, the unity and future of what has been known for 67 years as "postwar Europe" faces its biggest challenge ever. In the space of a few years, Europe has moved from bristling with confidence to a collective crisis that is shaking its unprecedented prosperity to the core.

What began as a debt crisis in Greece in late 2009 – a cloud the size of a fist – has grown into a thunderhead of fractious politics, extremism, costly delay, denials, ethnic tension, and, not least, an erosion of public trust that threatens the core values of Europe's remarkable postwar experiment in integration.

In America, the crisis is largely viewed as an economic story channeled through CNBC and Bloomberg – as some kind of euro mismanagement recorded on graphs and stock tickers. But the problem runs far deeper. It cuts to the core of what Europe may or may not become. It is a crisis of identity and politics with social fallout and, what scares many, an element of that old unknown: unintended consequences.

Extremist political parties are rising. Taxpayers are revolting in the north about bailing out the south. For the far left, "Europe" has become a protectionist zone for bankers and the moneyed class. For the far right, Europe is too tolerant of Muslims, Islam, and immigrants.

Yet Europe's crisis has crept along so slowly that it has been hard to know how seriously to take it. On Mondays, Wednesdays, and Fridays come predictions swathed in gloom. On Tuesdays, Thursdays, and Saturdays, the crisis can seem "illusory," as analyst Konstanty Gebert notes in Warsaw. (In resilient Eastern Europe, as some Baltic officials said this summer, a crisis is when the Soviet Union invades; what Europe is now dealing with is just a "problem.")

Part of Europe's hidden genius, as British historian David Marquand (no relation to this writer) says from his home in Oxford, "has been to be boring. Boring meant peace and no drama." Mr. Marquand, whose book "The End of the West: The Once and Future Europe" came out last year, adds, "Today, from inside the crisis, it is difficult to gauge where you are. I hope we have turned a corner. But I'm always worried about the rise of extremism."

Leading intellectuals now say the crisis is the most serious one since 1945. Arguably it carries more portent than even the halcyon days of 1989, when the Berlin Wall came down, simply because it is unclear if Europe can remain intact. And a breakup of Europe, even in slow motion, is big: It reverberates from St. Louis to Shanghai to São Paulo.

Dominique Moïsi, the leading Paris intellectual and author of "The Geopolitics of Emotion," points out that while Europe has not experienced such a severe crisis since World War II, "still I am positive. I would say that at the last minute, because they have exhausted all other options, Europeans are finally doing the right thing out of necessity, and in a strange manner. There is much more Europe today than there was a few years ago."

The next 12 months will be crucial in deciding if there is enough "Europe" to hold it all together. The Continent's fate will pivot on whether leaders can still see more rewards in unity than risks in dissolution – and convince their citizens of that. For the first time in European history, two generations have been born who have not experienced war, which was one of the great unifying factors in the birth of an integrated Europe.

"Now, with the current crisis still unresolved, Europe lacks most of the motivating forces that once propelled it toward unity," wrote British historian Timothy Garton Ash in the September/October issue of the journal Foreign Affairs. "Even if a shared fear of the consequences of the eurozone's collapse saves it from the worst, Europe needs something more than fear to make it again the magnetic project it was for a half century."

In October, the Nobel Committee gave the 2012 peace prize to the EU. The prize is an obvious acknowledgment of Europe's longest-ever peace. It is also a morale builder, an affirmative prod that EU nations and peoples not break up at this fragile moment in history.

* * *

Few saw a crisis coming. Five years ago no one could imagine Italy and Spain teetering on the brink of insolvency, or that "bailout" and "austerity" would be household words from Gdansk to Palermo. It would seem science fiction to say that in 2012 an openly neo-Nazi party, Golden Dawn in Greece, would capture 7 percent of the vote in a European election. Or that right-left extremes in France would garner nearly 40 percent of the vote, as they did in balloting this spring.

In 2007, talk of breakup, of bond markets "factoring in" possible departures from the eurozone, or of a Europe of the north and a Europe of the south, would have seemed absurd. Europe was cash rich, with banks lending at 1 percent.

Remember, too, that a decade ago, intellectuals on both sides of the Atlantic routinely described Europe – with a population of 500 million and a gross domestic product of $16 trillion – as "the future." American economic guru Jeremy Rifkin outlined a "European Dream" in which cherished values of justice would merge with social equity. Charles Kupchan of the Council on Foreign Relations predicted an inexorably integrating Europe as a global counterweight to the US. With America mired in a global war on terrorism, British author Mark Leonard wrote convincingly about the "Ascent of Europe."

(In an interview in London, Mr. Leonard, cofounder and director of the European Council on Foreign Relations, now argues that Europe's unwillingness to face the crisis head-on means "the best-case scenario is a lost decade.")

Perhaps, from an American perspective, the most striking and baffling aspect is this: Theoretically, Europe's crisis could be solved in five minutes, with a change of heart in Berlin and Brussels.

That is precisely what the best and the brightest have said in interviews in Germany, France, and Britain in recent months. Because this is a political crisis more than an economic crisis, Europe only has to take the next step in its historic process of integration. The problem is that integration, at bottom, means a sharing of debt – and this is where everything turns nationalistic.

What the current crisis exposes is the incompleteness of the 1999 creation of a common currency, the euro, without a common fiscal policy. A fiscal policy would require mutual obligations. Europe has, in effect, a "dollar" without a Federal Reserve.

That leaves the 17-member eurozone in the equivalent position of a US in which the states share the greenback, but each state rises or falls on its own – as if there were a Maine dollar, a Florida dollar, or a Texas dollar. EU states that are weaker, or face bad times, are left to fend for themselves. They are chained to the euro without the ability to devaluate.

The euro was fine in good economic times; its "flaws" have only shown up since the 2007 debt crisis. "They set up, with the euro, an arrangement they have to complete or it will fall apart. And if it falls apart, what then?" asks Philip Whyte, a senior fellow at the Centre for European Reform, a think tank in London. "The eurozone is a pillar of the EU. It is hard to imagine it can collapse without damage to the EU."

Yet unlike the first round of postwar European integration, which was achieved by its founders "on the sly," as it is said – in which for decades institutions were mashed together, forcing different peoples to work with a common purpose – the "next step" of integration will have to be a more conscious decision, analysts say, taken in full public view.

At the center of the issue is Germany. Postwar Germany was the most European of EU states as it confronted its Nazi past. But times have changed; it is unclear whether the public in Europe's most dynamic and unified country is willing to shoulder more of the burden. (More on this later.)

Without clear solidarity in Europe, and with economies contracting under an EU prescription of austerity, bond markets attack weak or debtor nations. Without a mutual feeling of states helping each other, a new cynicism is taking root among ordinary people and elites alike.

Since the 2010 Greek trauma, the EU has held no fewer than 19 mind-numbing crisis talks in Brussels, out of which 27 state leaders have spun their own often widely differing interpretations. Financial markets have not been impressed. Five governments have fallen.

Spain, the fourth-largest economy in the eurozone, is still looking into the abyss. Its unemployment rate stands at 24 percent – 53 percent among youths. The positions and solvency of Portugal, Ireland, and Italy remain tenuous. New French President François Hollande faces 3 million unemployed.

A surly spirit seems to pervade everything. Greeks call Germans Nazis, and German tabloids mock Greeks as lazy. Newspapers and corporations fret about China and Brazil eclipsing Europe. Brussels, the EU capital, is depicted as a heartless technocratic machine.

In cafes, a certain fatalistic chat is fashionable about whether the situation is more like 1930 (the beginning of the Great Depression) or 1939 (the eve of Nazi aggression). Robin Niblett, director of Chatham House, a London-based think tank, suggests another period: "My gamble or risky call is that we will look at this in 15 years 'time and it will look more like the 1970s than the 1920s or '30s. The 1970s were a nasty difficult dark period for Europe, but not [as bad as] the 1930s, and they got through it."

So we are back in some ways to the Olympics example: Can Europe's political athletes run and swim for the EU as well as for their own nations? Can Europe summon the spirit, morale, and motivation to hang together, or will it increasingly "hang separately," to use the phrase coined in Colonial America?

* * *

In a very real sense, today's EU emerged from the wars and nationalism that cleaved the Continent between 1914 and 1945 and continued to divide Europe until 1989. It was only last year that the final living French soldier who fought in World War I died.

As a particularly cathartic moment, look no further than Verdun, 90 minutes east by train and bus from Paris. Lying next to a river in a pleasant valley, it is the site of the most hellish battle in European history, in 1916. Verdun is both a reminder of the impulse to "end all wars," and of the origins of a federally integrated EU. The battle, 300 intense days and nights, took place up a hilly incline. "It was supposed to last six weeks," says local guide Ingrid Ferrand, a German woman married to a French officer. "Instead, for months, the fate of France turned here."

"It is probably no exaggeration to call Verdun the 'worst' battle in history; even taking into account man's subsequent endeavors in the Second World War," writes Alistair Horne in "The Price of Glory: Verdun 1916." "Verdun was the First War in microcosm; an intensification of all its horrors and glories, courage and futility."

Nine local villages were eviscerated; 700,000 men were killed. At the end, as the sepia photos show, not a tree stood for miles over a moonscape whose topsoil was blasted out by 6 million shells.

Today, the site retains a sober aura, with mostly German tourists coming with cameras. The famed battle trenches, from which wave after wave of soldiers lunged, often to capture only a few yards of territory, are largely filled in.

The psychological effect of Verdun lasted well into the 20th century. Only in 1984 did Germany's Helmut Kohl and France's François Mitterrand shake hands here in what has become a famous photo of the era. The humiliation of the peace terms at Versailles in 1919 led to Nazism and the second installment of Armageddon on the Continent.

Those wars now exist mostly as movie reels in Europe's imagination. French and Germans no longer hate each other; despite, or because of, all that happened, there was a reconciliation.

Now the EU will have to surmount its economic and political "wars," which pivot mainly on two centers of power – Berlin, foremost, but also Paris. In the past year, EU officials in crisis meetings have described Angela Merkel and Nicolas Sarkozy leaving the room, huddling, and coming back to prescribe the final decision. (This has not been repeated with Mr. Hollande.)

Germany's size and clout allow it to dictate the pace and direction of the eurozone. In interviews in which experts offer quick resolutions to the crisis, the comments usually center on the political will and winds in Berlin. The German people remain worried about inflation, about losing their competitive edge, and about being mired in debt. Yet, on the whole, Germans have not accepted that their legendary export success, while tied strongly to sales in Asia, also benefits from European buyers.

"There is no conviction yet that Germany is willing to commit to the kind of mutualization of debt that is fundamental to the survival of the euro," says Dr. Niblett at Chatham House. "They define Europe's collective responsibility rather than solidarity. That means: 'We are all in this together; therefore, we must all be responsible,' not, 'We are all in this together, so we need to help each other out.' Making that transition from the former to the latter has not yet happened in Germany."

American billionaire George Soros, in a recent New York Review of Books piece, "The Tragedy of the European Union and How to Resolve It," says that Germany must either "lead or leave" Europe. The current German-led approach of solving the crisis piecemeal and by applying rules meant to reform countries' behavior and finances in the long term is not sustainable.

Yet the idea of Germany "leaving" the eurozone is so fraught, is such a denial of its postwar identity, that few analysts believe this can or will happen. Opinion is also divided over whether Berlin really wants to see Greece stay in the eurozone. While Greece represents less than 2 percent of Europe's GDP, its status is seen as central to the future of the Union. A Greek departure would likely have a catastrophic effect on financial markets because of what it portends for Spain and Italy, two nations whose stability Europe can't do without.

Some analysts believe that Germany will let Greece leave in return for accepting mutualized debt. Yet Western diplomats familiar with Chancellor Merkel say she has resolved to keep Greece in the Union. At some point in the summer of 2011, according to a diplomat in Berlin, Merkel saw that Europe had to stay intact and decided she would not be blamed or preside over the undoing of Europe after 60 years.

"She's alone right now at the top. She knows she is the Adenauer of this hour," says the diplomat, referring to the leader who helped rebuild postwar Germany, "and she knows she is a historical figure. She wants to keep Greece in, and she wants to keep Europe together."

Still, the anger outside Germany is growing. Spain is a case in point. Prime Minister Mariano Rajoy agreed to a bailout in June, thinking that, in return, the EU would "collectivize" some €60 billion ($78 billion) in debt – in other words, that one of the two bailout stability mechanisms, the European Social Fund or the European Stability Mechanism, would cover it.

"Rajoy wanted to keep €60 billion off the books," says John Hulsman, a global political consultant who lives near Frankfurt. "And that's the deal Spain signed on to. But Merkel has now turned around [in September] to say the agreement is only good for future debt. That's a betrayal. It's another €60 billion for a country already falling out of the sky economically."

"I think we are in Act III of a vampire drama," adds Mr. Hulsman, "and there is no closing act in sight."

* * *

In central Berlin, under a typically brilliant blue sky in October, students are buying waffles and strawberries at a cafe. Across the street, giant drills gnaw away at a construction project designed to rebuild the Weimar-era palace. A bilingual sign outside describes it as "the largest cultural project in Europe."

"There is no sense of crisis here," says a German political official who requested anonymity. "Or, if there is one, it is blamed on lazy Greeks. Fifty percent unemployment in Spain seems very theoretical in this climate. Angela [Merkel] is like a mother figure; I mean that literally. Germans think she is looking out for their interests, keeping them safe."

In London, Leonard describes the current period as an interregnum in which creditor and debtor nations are hunkering down and waiting on events. "Germans are using the crisis to do what they regard to be in their best interest, namely, their homework. Be competitive, reform.... They want to use the crisis to extract the maximum amount of concessions – and that could go wrong: They could miscalculate."

In the past month, several developments have surfaced that suggest at least some crisis amelioration is under way across the Continent. Mario Draghi, president of the European Central Bank, has promised to "do whatever it takes" to save the euro. Dutch voters did not give a predicted electoral victory to Geert Wilders, the leader of a far-right anti-Islam and anti-Europe party. Several key working groups of foreign ministers and of the EU commission are charting serious political reforms, such as a banking union, really for the first time ever.

Moves like these, coupled with Europe's deeper bonds and shared sense of history, make many experts believe the Continent will ultimately surmount its problems, even if the process is prolonged and painful.

"The prediction about the death of Europe is greatly exaggerated," says Mr. Moïsi. "Go to Asia and no one says they are Asian. They are Japanese and Chinese. But in Europe, we are European. We are no longer a 'project'; we are a reality."

Indeed, Europe's postwar founders would see in the vast intermeshing of EU nations a success story far greater than they could have imagined. On any given day, Polish trucks lumber along France's A6 highway. Some 1.6 million Eastern Europeans live and work in Dublin, Ireland; and London. There's what has come to be known as the "easyJet phenomenon," meaning that for usually less than €100 one can travel to almost any city in Europe. EU leaders may talk of needing "more Europe," but on the ground, it is already happening in countless iterations.

European products from machine tools to cosmetics are prized around the world. Literacy is high. If you discount the current divisive political crisis posing as a euro crisis, many of Europe's economic fundamentals, from savings to trade, are better than those of the US.

"The narrative of the last two years that Europe is slowly collapsing – well, let's see how things pan out," says Niblett. "One narrative is that finally European governments are doing what they should have done 10 years ago. You now have labor laws in Spain. You have new controls. The trucking licenses in Greece have been torn up and thrown away – the kind of structural reform that has been talked about for years but has never happened because everyone was living in la-la land and thought interest rates of 1 percent meant everyone was rich when they weren't ... that delusion has been thoroughly obliterated. People are now in a crash course having to do what Europe should have chosen to do long back."

Europe also has a different history, rarely told, of progress, invention, healthy dissent, art and letters, and of promoting universal values. Europeans have usually tried to escape a history of poisonous nationalism, and Verdun and Auschwitz and shame have paved over what Marquand calls its "history of common values ... of a cultured, cosmopolitan, liberal bourgeoisie, moving easily between Paris, Vienna, Prague, Warsaw, and Berlin...."

Cosmopolitan Europe emerged in cafes and universities both during the Enlightenment and during the belle epoque at the turn of the last century. It's one stereotype in the American imagination that happens to be true. Artists, scientists, bohemians, editors, novelists, and dissidents met amid piles of newspapers and cheap coffee. In these urban zones of creative ferment, they debated new ideas. The concept of a continent unfettered by hate and borders, by violence and will, checkpoints and nationalism, was touted by literary lions like Austrian Stefan Zweig and Frenchman Romain Rolland.

Today, the vision and dreams of such writers have been, in a sense, democratized. What seemed utopian in the 1920s is now almost mundane. A common civic space – a shared zone between government and corporations – endures in Europe, partly as the notion of an open society. As Marquand puts it, the creation of the EU "is a successful protest against boundaries and also against history."

In a provocative essay last year, eminent German philosopher Jürgen Habermas wrote about the "long shadow cast by nationalism" in Europe. He wondered how Europeans, with or without their political elites, could generate the enthusiasm to help each other out.

Yet despite the current economic chaos and his despair at the response to it by Germany, which he says since 1989 has been ruled by a "morally unambitious generation," Mr. Habermas, too, remains hopeful. At the core, he argues, in slightly utopian style, that "human dignity" will win out. Europe's traditions of law and rights, along with globalization and diversity, and Internet penetration, will awaken a common-sense "universalism" among citizens.

Niblett is more pragmatic but no less passionate in his views of why Europe will stay together. Facing the rise of Asia, which has its own dark history of competition and conflict, the costs of disunity and failure would simply be too catastrophic. "A unified Europe isn't a matter of choice, something nice to have," he says. "There is no choice. It may be messy and painful. But we can't go back."